%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : BOO013-2 : TPTP v8.1.0. Bugfixed v1.2.1. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n017.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Thu Jul 14 23:46:25 EDT 2022 % Result : Unsatisfiable 8.97s 8.88s % Output : Proof 8.97s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : BOO013-2 : TPTP v8.1.0. Bugfixed v1.2.1. % 0.12/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n017.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Wed Jun 1 14:34:57 EDT 2022 % 0.20/0.34 % CPUTime : % 8.97/8.88 % SZS status Unsatisfiable % 8.97/8.88 % SZS output start Proof % 8.97/8.88 The input problem is unsatisfiable because % 8.97/8.88 % 8.97/8.88 [1] the following set of Horn clauses is unsatisfiable: % 8.97/8.88 % 8.97/8.88 add(X, Y) = add(Y, X) % 8.97/8.88 multiply(X, Y) = multiply(Y, X) % 8.97/8.88 add(multiply(X, Y), Z) = multiply(add(X, Z), add(Y, Z)) % 8.97/8.88 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)) % 8.97/8.88 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)) % 8.97/8.88 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 8.97/8.88 add(X, inverse(X)) = multiplicative_identity % 8.97/8.88 add(inverse(X), X) = multiplicative_identity % 8.97/8.88 multiply(X, inverse(X)) = additive_identity % 8.97/8.88 multiply(inverse(X), X) = additive_identity % 8.97/8.88 multiply(X, multiplicative_identity) = X % 8.97/8.88 multiply(multiplicative_identity, X) = X % 8.97/8.88 add(X, additive_identity) = X % 8.97/8.88 add(additive_identity, X) = X % 8.97/8.88 add(a, b) = multiplicative_identity % 8.97/8.88 add(a, c) = multiplicative_identity % 8.97/8.88 multiply(a, b) = additive_identity % 8.97/8.88 multiply(a, c) = additive_identity % 8.97/8.88 b = c ==> \bottom % 8.97/8.88 % 8.97/8.88 This holds because % 8.97/8.88 % 8.97/8.88 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 8.97/8.88 % 8.97/8.88 E: % 8.97/8.88 add(X, Y) = add(Y, X) % 8.97/8.88 add(X, additive_identity) = X % 8.97/8.88 add(X, inverse(X)) = multiplicative_identity % 8.97/8.88 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)) % 8.97/8.88 add(a, b) = multiplicative_identity % 8.97/8.88 add(a, c) = multiplicative_identity % 8.97/8.88 add(additive_identity, X) = X % 8.97/8.88 add(inverse(X), X) = multiplicative_identity % 8.97/8.88 add(multiply(X, Y), Z) = multiply(add(X, Z), add(Y, Z)) % 8.97/8.88 f1(b) = true__ % 8.97/8.88 f1(c) = false__ % 8.97/8.88 multiply(X, Y) = multiply(Y, X) % 8.97/8.88 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 8.97/8.88 multiply(X, inverse(X)) = additive_identity % 8.97/8.88 multiply(X, multiplicative_identity) = X % 8.97/8.88 multiply(a, b) = additive_identity % 8.97/8.88 multiply(a, c) = additive_identity % 8.97/8.88 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)) % 8.97/8.88 multiply(inverse(X), X) = additive_identity % 8.97/8.88 multiply(multiplicative_identity, X) = X % 8.97/8.88 G: % 8.97/8.88 true__ = false__ % 8.97/8.88 % 8.97/8.88 This holds because % 8.97/8.88 % 8.97/8.88 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 8.97/8.88 % 8.97/8.88 add(X, Y) = add(Y, X) % 8.97/8.88 multiply(X, Y) = multiply(Y, X) % 8.97/8.88 add(X, additive_identity) -> X % 8.97/8.88 add(X, inverse(X)) -> add(a, c) % 8.97/8.88 add(Y0, multiply(a, b)) -> Y0 % 8.97/8.88 add(Y0, multiply(a, c)) -> Y0 % 8.97/8.88 add(a, a) -> a % 8.97/8.88 add(additive_identity, X) -> X % 8.97/8.88 add(b, inverse(a)) -> inverse(a) % 8.97/8.88 add(c, b) -> c % 8.97/8.88 add(c, c) -> c % 8.97/8.88 add(c, inverse(a)) -> inverse(a) % 8.97/8.88 add(inverse(X), X) -> add(a, c) % 8.97/8.88 add(multiply(Y0, a), multiply(Y0, c)) -> Y0 % 8.97/8.88 add(multiply(a, Y0), multiply(c, Y0)) -> Y0 % 8.97/8.88 add(multiply(a, b), Y0) -> Y0 % 8.97/8.88 add(multiply(a, b), multiply(a, multiply(a, b))) -> multiply(a, c) % 8.97/8.88 add(multiply(a, c), Y0) -> Y0 % 8.97/8.88 additive_identity -> multiply(a, c) % 8.97/8.88 b -> c % 8.97/8.88 f1(b) -> true__ % 8.97/8.88 f1(c) -> false__ % 8.97/8.88 inverse(add(a, c)) -> multiply(a, c) % 8.97/8.88 inverse(multiply(a, c)) -> add(a, c) % 8.97/8.88 multiplicative_identity -> add(a, c) % 8.97/8.88 multiply(X, add(Y, Z)) -> add(multiply(X, Y), multiply(X, Z)) % 8.97/8.88 multiply(X, inverse(X)) -> multiply(a, c) % 8.97/8.88 multiply(a, multiply(a, c)) -> multiply(a, c) % 8.97/8.88 multiply(add(X, Y), Z) -> add(multiply(X, Z), multiply(Y, Z)) % 8.97/8.88 multiply(add(X, Y), add(X, Z)) -> add(X, multiply(Y, Z)) % 8.97/8.88 multiply(add(X, Z), add(Y, Z)) -> add(multiply(X, Y), Z) % 8.97/8.88 multiply(add(Y0, Y2), add(add(a, b), Y2)) -> add(Y0, Y2) % 8.97/8.88 multiply(add(Y0, Y2), add(add(a, c), Y2)) -> add(Y0, Y2) % 8.97/8.88 multiply(add(Y0, a), add(Y0, b)) -> Y0 % 8.97/8.88 multiply(add(Y0, a), add(Y0, c)) -> Y0 % 8.97/8.88 multiply(add(Y0, a), add(b, Y0)) -> Y0 % 8.97/8.88 multiply(add(Y0, a), add(c, Y0)) -> Y0 % 8.97/8.88 multiply(add(a, Y0), add(Y0, b)) -> Y0 % 8.97/8.88 multiply(add(a, Y0), add(Y0, c)) -> Y0 % 8.97/8.88 multiply(add(a, Y0), add(b, Y0)) -> Y0 % 8.97/8.88 multiply(add(a, Y0), add(c, Y0)) -> Y0 % 8.97/8.88 multiply(add(a, Y0), multiply(add(Y0, Y0), add(Y0, b))) -> Y0 % 8.97/8.88 multiply(add(a, Y0), multiply(add(Y0, Y0), add(Y0, c))) -> Y0 % 8.97/8.88 multiply(b, b) -> c % 8.97/8.88 multiply(c, c) -> c % 8.97/8.88 multiply(inverse(X), X) -> multiply(a, c) % 8.97/8.88 multiply(multiply(add(Y0, b), add(Y0, Y0)), add(a, Y0)) -> Y0 % 8.97/8.88 multiply(multiply(add(Y0, c), add(Y0, Y0)), add(a, Y0)) -> Y0 % 8.97/8.88 true__ -> false__ % 8.97/8.88 with the LPO induced by % 8.97/8.88 f1 > inverse > additive_identity > multiplicative_identity > b > c > multiply > add > a > true__ > false__ % 8.97/8.88 % 8.97/8.88 % SZS output end Proof % 8.97/8.88 %------------------------------------------------------------------------------